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A remark on fixed point sets of gradient-like flows

Yuli Rudyak
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Abstract

Let $S$ be a set of critical points of a smooth real-valued function on a closed manifold $M$. Generalizing a well-known result of Lusternik--Schnirelmann, Reeken~[R] proved that $\cat S \geq \cat M$. Here we prove a generalization of Reeken"s inequality for gradient-like flows on compact spaces.

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Yuli Rudyak. 1999-08-04. A remark on fixed point sets of gradient-like flows. https://arxiv.org/abs/math/9908017

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